??????? ? (a) Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750ml size is q = 4000 − 250p and his total cost function is C(q) = XXXXXXXXXX2q. (i) Derive an...

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(a) Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750ml size is q = 4000 − 250p and his total cost function is C(q) = 500 + 0.2q.
(i) Derive an expression, R(q) for Teddy J′s total revenue curve.
(ii) Derive an expression, Π(q) for Teddy J′s profit function.
(iii) Determine whether Teddy J′s profit is increasing or decreasing when
he produces 5 hundred, 750ml bottles of dish washing liquid.
(iv) How many 750ml bottles of dish washing liquid should Teddy J produce
per month if he wishes to maximize his profits.

(b) A firm has an average cost function
A(q) =125 + q²
    - 4
            q      16


where q is the firm′s output.
(i) Determine the level of output for average costs are minimum.
(ii) Hence determine the range of values for which average costs are decreasing.
(iii) What part of the decreasing range is practically feasible?
(iv) Write an equation for the total cost function.
(v) Hence calculate the level of output for which total costs are minimum.